Heat the vegetable oil in a large pot over medium heat. Add the diced onion and cook for 4 minutes until it softens.
Stir in the minced garlic, bruised lemongrass pieces, and grated ginger. Cook for 1 minute until fragrant.
Add the sliced chicken sausage and cook for 5 minutes, stirring occasionally, until the pieces begin to brown.
Pour in the rinsed green lentils and chicken broth. Bring the mixture to a boil, then reduce to a simmer.
Cover and cook for 25 minutes, stirring once or twice, until the lentils are tender.
Stir in the coconut milk and fish sauce. Simmer uncovered for 5 more minutes.
Remove the lemongrass pieces, then stir in the lime juice. Ladle into bowls and top with chopped cilantro.